Triple

T11576265
Position Surface form Disambiguated ID Type / Status
Subject Joseph Bernstein E274511 entity
Predicate notableWork P4 FINISHED
Object Bernstein–Sato polynomial
The Bernstein–Sato polynomial is a fundamental object in algebraic analysis and singularity theory that encodes deep information about the behavior of functions and their singularities via differential equations.
E934438 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Bernstein–Sato polynomial | Statement: [Joseph Bernstein, notableWork, Bernstein–Sato polynomial]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bernstein–Sato polynomial
Context triple: [Joseph Bernstein, notableWork, Bernstein–Sato polynomial]
  • A. Hilbert polynomial
    The Hilbert polynomial is an algebraic invariant that encodes the asymptotic growth of the dimension of graded components of a module or the number of independent conditions imposed by a projective variety.
  • B. Symanzik polynomials
    Symanzik polynomials are graph-based polynomials that arise in the parametric representation of Feynman integrals in quantum field theory, encoding the topology and kinematic dependence of Feynman diagrams.
  • C. Singular Points of Complex Hypersurfaces
    "Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
  • D. Hilbert’s fourteenth problem
    Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
  • E. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Bernstein–Sato polynomial
Triple: [Joseph Bernstein, notableWork, Bernstein–Sato polynomial]
Generated description
The Bernstein–Sato polynomial is a fundamental object in algebraic analysis and singularity theory that encodes deep information about the behavior of functions and their singularities via differential equations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bernstein–Sato polynomial
Target entity description: The Bernstein–Sato polynomial is a fundamental object in algebraic analysis and singularity theory that encodes deep information about the behavior of functions and their singularities via differential equations.
  • A. Hilbert polynomial
    The Hilbert polynomial is an algebraic invariant that encodes the asymptotic growth of the dimension of graded components of a module or the number of independent conditions imposed by a projective variety.
  • B. Symanzik polynomials
    Symanzik polynomials are graph-based polynomials that arise in the parametric representation of Feynman integrals in quantum field theory, encoding the topology and kinematic dependence of Feynman diagrams.
  • C. Singular Points of Complex Hypersurfaces
    "Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
  • D. Hilbert’s fourteenth problem
    Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
  • E. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d6aae5ac3c81908d2b0a3a665665b2 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d89049721081909278adfada668ef9 completed April 10, 2026, 5:53 a.m.
NED1 Entity disambiguation (via context triple) batch_69e713f7ca4c81908f29143df420fd71 completed April 21, 2026, 6:06 a.m.
NEDg Description generation batch_69e720f9a8588190aa766d2e1628207a completed April 21, 2026, 7:02 a.m.
NED2 Entity disambiguation (via description) batch_69e72315dda08190996aa84587c5fc80 completed April 21, 2026, 7:11 a.m.
Created at: April 8, 2026, 9:38 p.m.